2018 cfa Level 3 Wiley Formula SheetDescription complète
2018 cfa Level 3 Wiley Formula Sheet
Description : This section contains note of CFA level 2 Program
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C r i t i c a l C o n c e pt d
ETHICAL AND PROFESSIONAL STANDARDS ___________________________________________________________________________________________________________
I 1(A) 1(B) 1(C) 1(D) II 11(A) 11(B) III III (A) III(B) III(C) III(D) III(E) IV IV(A) IV(B) IV(C) V V(A) V(B) V(C) VI VI (A) VI(B) VI (C) VII VII(A) VII(B)
Professionalism Knowledge of the Law. Independence and Objectivity. Misrepresentation. Misconduct. Integrity of Capital Markets Material Nonpublic Information. Market Manipulation. Duties to Clients Loyalty, Prudence, and Care. Fair Dealing. Suitability. Performance Presentation. Preservation of Confidentiality. Duties to Employers Loyalty. Additional Compensation Arrangements. Responsibilities of Supervisors. Investment Analysis, Recommendations, and Actions Diligence and Reasonable Basis. Communication with Clients and Prospective Clients. Record Retention. Conflicts of Interest Disclosure of Conflicts. Priority of Trans actio ns. Referral Fees. Responsibilities as a CFA Institute Member or CFA Candidate Conduct as Participants in CFA Institute Programs. Reference to CFA Institute, the CFA Designation, and the CFA Program.
Global Investment Performance Standards (GIPS®) • Compliance statement: “ [Insert name of firm] has prepared and presented this report in compliance with the Global Investment Performance Standards (GIPS).” Compliance must be applied on a firm-wide basis. • Nine sections: fundamentals of compliance, input data, calculation methodology, composite construction, disclosures, presentation and reporting, real estate, private equity, and wrap fee/separately managed account portfolios.
2018 CFA® E x a m
s for t he
Approximation formula for nominal required rate: E(R) = RFR + IP + RP
E ( R P) =
Means Arithmetic mean: sum of all observation values in sample/population, divided by # of observations. Geometric mean: used when calculating investment returns over multiple periods or to measure compound growth rates. Geometric mean return:
Rc= (1 + R,)x...x(l + RN) P - 1 harmonic mean = N
Expected return, variance o f 2-stock portfolio:
E i=i .5 c , V
Variance and Standard Deviation Variance: average of squared deviations from mean.
population variance = cr = — -----N n
sample variance - s2- i=i
x)2 n —1
Standard deviation: square root of variance. H olding Period Return (HPR) P , - P ^ + D,
Coefficient o f Variation Coefficient o f variation (CV): expresses how much dispersion exists relative to mean of a distribution; allows for direct comparison of dispersion across different data sets. CV is calculated by dividing standard deviation of a distribution by the mean or expected value of the distribution:
cv = 4 X
Sharpe Ratio Sharpe ratio: measures excess return per unit of risk. Sharpe ratio =
rP ~ rf
E(R a ) +
w b E(Rb)
Var( R p) = WAa 2 (R a ) + W2B<72 ( R b )
+ 2 w a w b
Computing Z-Scores Z-score: “standardizes” observation from normal distribution; represents # of standard deviations a given observation is from population mean. z=
observation —population mean
Binomial Models Binomial distribution: assumes a variable can take one of two values (success/failure) or, in the case of a stock, movements (up/down). A binomial model can describe changes in the value of an asset or portfolio; it can be used to compute its expected value over several periods. Sampling Distribution Sampling distribution: probability distribution of all possible sample statistics computed from a set of equal-size samples randomly drawn from the same population. The sampling distribution o f the mean is the distribution of estimates of the mean. Central Limit Theorem Central lim it theorem: when selecting simple random samples of size n from population with mean p, and finite variance a 2, the sampling distribution of sample mean approaches normal probability distribution with mean |i and variance equal to o2ln as the sample size becomes large. Standard Error Standard error o f the sample mean is the standard deviation of distribution of the sample means. known population variance: cr- =
QUANTITATIVE METHODS Time Value o f M oney Basics • Future value (FV): amount to which investment grows after one or more compounding periods. • Future value: FV = PV(1 + I/Y)N. • Present value (PV): current value of some future cash flow PV = FV/(1 + I/Y)N. • Annuities: series of equal cash flows that occur at evenly spaced intervals over time. • Ordinary annuity: cash flow at ^W-of-time period. • Annuity due: cash flow at beginning-of-time period. • Perpetuities: annuities with infinite lives. PVperpetuity . = PMT/(discount rate). v ' Required Rate o f Return Components: 1. Real risk-free rate (RFR). 2. Expected inflation rate premium (IP). 3. Risk premium.
E(R) = (l + RFRreal)(l + IP)(l + RP) —1
Roy’s safety-first ratio:
For both ratios, larger is better. Expected Return/Standard Deviation Expected return: E(X ) = ^ ^ P ( x j) xn E(X ) = P (x1)x 1+ P ( x 2)x 2 + . . . + P (xn)x n Probabilistic variance'. a 2( X ) = y > ( x i ) [ x i - E ( X ) f
unknown population variance: s? = Confidence Intervals Confidence interval: gives range of values the mean value will be between, with a given probability (say 90% or 95%). With known variance, formula for a confidence interval is: x ± za l l Za/2
Standard deviation: take square root of variance. Correlation and Covariance Correlation: covariance divided by product of the two standard deviations.
a -r b )
Normal Distributions Normal distribution is completely described by its mean and variance. 68% of observations fall within ± la . 90% fall within ± 1.65a. 95% fall within ± 1.96a. 99% fall within ± 2.58a.
1.645 for 90% confidence intervals (significance level 10%, 5% in each tail) 1.960 for 95% confidence intervals (significance level 5%, 2.5% in each tail) 2.575 for 99% confidence intervals (significance level 1%, 0.5% in each tail)
N ull and Alternative Hypotheses N ull hypothesis (HQ): hypothesis that contains the equal sign (=, <, >); the hypothesis that is actually tested; the basis for selection of the test statistics. Alternative hypothesis (Ha): concluded if there is sufficient evidence to reject the null hypothesis. Difference Between One- and Two-Tailed Tests One-tailed test: tests whether value is greater than or less than a given number. Two-tailed test: tests whether value is equal to a given number. • One-tailed test: Ho: p < 0 versus H a: p > 0. • Two-tailed test: Ho: p = 0 versus H a: p * 0. Type I and Type II Errors • Type I error: rejection of null hypothesis when it is actually true. • Type II error: failure to reject null hypothesis when it is actually false. Types o f Hypothesis Tests Use t-statistic for tests involving the population mean (location of mean, difference in means, paired comparisons). Use chi-square statistic for tests of a single population variance. Use F-statistic for tests comparing two population variances. Technical Analysis Reversal patterns: head and shoulders, inverse H&S, double/triple top or bottom. Continuation patterns: triangles, rectangles, pennants, flags. Price-based indicators: moving averages, Bollinger bands, momentum oscillators (rate of change, RSI, stochastic, MACD). Sentiment indicators: opinion polls, put/call ratio, VIX, margin debt, short interest ratio. Flow o f funds indicators: TRIN, margin debt, mutual fund cash position, new equity issuance, secondary offerings.
ECONOMICS Elasticity _ . . . . %A quantity demanded Own price elasticity = ------- -------- — -----------%A price If absolute value > 1, demand is elastic. If absolute value < 1, demand is inelastic. O n a straight line demand curve, total revenue is maximized where price elasticity = —1. T , . . %A q uantity demanded income elasticity = ------ -------- -J-------------%A income If positive, the good is a normal good. If negative, the good is an inferior good. _ . . . . %A quantity demanded Cross price elasticity = ------- — m ------ --------------%A price of related good If positive, related good is a substitute. If negative, related good is a complement. Breakeven and Shutdown Breakeven: total revenue = total cost. Operate in short run if total revenue is greater than total variable cost but less than total cost. Shut down in short run if total revenue is less than total variable cost. Market Structures Perfect competition: Many firms with no pricing power; very low or no barriers to entry; homogeneous product. Monopolistic competition: Many firms; some pricing power; low barriers to entry; differentiated products; large advertising expense.
Oligopoly: Few firms that may have significant pricing power; high barriers to entry; products may be homogeneous or differentiated. Monopoly: Single firm with significant pricing power; high barriers to entry; advertising used to compete with substitute products. In all market structures, profit is maximized at the output quantity for which marginal revenue = marginal cost. Gross D om estic Product Real GDP = consumption spending + investment + government spending + net exports. Savings, Investment, Fiscal Balance, and Trade Balance Fiscal budget deficit (G —T) = excess of saving over domestic investment (S —I) —trade balance (X —M) Equation o f Exchange MV = PY, where M = real money supply, V = velocity of money in transactions, P = price level, and Y = real GDP. Business Cycle Phases Expansion; peak; contraction; trough. Economic Indicators Leading: Turning points occur ahead of peaks and troughs (stock prices, initial unemployment claims, manufacturing new orders) Coincident: Turning points coincide with peaks and troughs (nonfarm payrolls, personal income, manufacturing sales) Lagging: Turning points follow peaks and troughs (average duration of unemployment, inventory/ sales ratio, prime rate) Factors Affecting Aggregate Demand Consumers’ wealth; business expectations; consumers’ income expectations; capacity utilization; monetary and fiscal policy; exchange rates; global economic growth. Factors Affecting SR Aggregate Supply Input prices; labor productivity; expectations for output prices; taxes and subsidies; exchange rates; all factors that affect LR aggregate supply. Factors Affecting LR Aggregate Supply Size of labor force; human capital; supply of natural resources; stock of physical capital; level of technology. Types o f Unemployment Frictional: time lag in matching qualified workers with job openings. Structural: unemployed workers do not have the skills to match newly created jobs. Cyclical: economy producing at less than capacity during contraction phase of business cycle. Policy Multipliers money multiplier = --------------- ---------reserve requirement fiscal multiplier = -------- — -------l-M P C (l-t) where M PC = marginal propensity to consume, t = tax rate. Expansionary and Contractionary Policy Monetary policy is expansionary when the policy rate is less than the neutral interest rate (real trend rate of economic growth + inflation target) and contractionary when the policy rate is greater than the neutral interest rate. Fiscal policy is expansionary when a budget deficit is increasing or surplus is decreasing, and contractionary when a budget deficit is decreasing or surplus is increasing.
Balance o f Payments Current account: merchandise and services; income receipts; unilateral transfers. Capital account: capital transfers; sales/purchases of nonfinancial assets. Financial account: government-owned assets abroad; foreign-owned assets in the country. Regional Trading Agreements Free trade area: Removes barriers to goods and services trade among members. Customs union: Members also adopt common trade policies with non-members. Common market: Members also remove barriers to labor and capital movements among members. Economic union: Members also establish common institutions and economic policy. Monetary union: Members also adopt a common currency. Foreign Exchange Rates For the exam, FX rates are expressed as price currency / base currency and interpreted as the number of units of the price currency for each unit of the base currency. Real Exchange Rate = nominal FX ra te X
Exchange Rate Regimes Formal dollarization: country adopts foreign currency. Monetary union: members adopt common currency. Fixed peg: ± 1% margin versus foreign currency or basket of currencies. Target zone: Wider margin than fixed peg. Crawling peg: Pegged exchange rate adjusted periodically. Crawling bands: W idth of margin increases over time. Managedfloating: Monetary authority acts to influence exchange rate but does not set a target. Independently floating: Exchange rate is marketdetermined.
F in a n c ia l .ANALYSIS
r ep o r t in g a n d
Revenue Recognition Two requirements: (1) completion of earnings process and (2) reasonable assurance of payment. Revenue Recognition Methods • Percentage-of-completion method. • Completed contract method. • Installment sales. • Cost recovery method. Converged Standards Issued May 2014 Five-step revenue recognition model: 1. Identify contracts 2. Identify performance obligations 3. Determine transaction price 4. Allocate price to obligations 5. Recognize when (as) obligations are satisfied Unusual or Infrequent Items • Gains/losses from disposal of a business segment. • Gains/losses from sale of assets or investments in subsidiaries. • Provisions for environmental remediation.
Impairments, write-offs, write-downs, and restructuring costs. • Integration expenses associated with businesses recendy acquired. Discontinued Operations To be accounted for as a discontinued operation, a business— assets, operations, investing, financing activities— must be physically/operationally distinct from rest of firm. Income/losses are reported net of tax after net income from continuing operations. Compute Cash Flows From Operations (CFO) Direct method: start with cash collections (cash equivalent of sales); cash inputs (cash equivalent of cost of goods sold); cash operating expenses; cash interest expense; cash taxes. Indirect method: start with net income, subtracting back gains and adding back losses resulting from financing or investment cash flows, adding back all noncash charges, and adding and subtracting asset and liability accounts that result from operations. Free Cash Flow Free cash flow (FCF) measures cash available for discretionary purposes. It is equal to operating cash flow less net capital expenditures. Critical Ratios Common-size financial statement analysis: • Common-size balance sheet expresses all balance sheet accounts as a percentage of total assets. • Common-size income statement expresses all income statement items as a percentage of sales. • Common-size cash flow statement expresses each line item as a percentage of total cash inflows (outflows), or as a percentage of net revenue. Horizontal common-sizefinancial statement analysis: expresses each line item relative to its value in a common base period. Liquidity ratios: current assets current ratio = ---------- ;—77-7— current liabilities cash + marketable securities + receivables quick ratio = current liabilities cash ratio =
cash + marketable securities current liabilities
defensive interval =
cash + mkt. sec. -j- receivables daily cash expenditures
Receivables, inventory, payables turnover, and days’ supply ratios— all o f which are used in the cash conversion cycle: . .. annual sales receivables turnover = ---------------;------average receivables cost of goods sold inventory turnover = --------- ------------average inventory payables turnover ratio =
days of sales outstanding =
365 receivables turnover
365 days of inventory on hand = 7 inventory turnover number of days of payables =
cash conversion cycle = +
days of sales outstanding
________365________ payables turnover ratio
days of inventory on hand
number of days of payables
Inventory Accounting In periods of rising prices and stable or increasing inventory quantities:
fixed asset turnover =
average fixed assets
working capital turnover =
LIFO results in: FIFO results in: Higher COGS Lower COGS Lower gross profit Higher gross profit Lower inventory Higher inventory balances balances Basic and D iluted EPS Basic EPS calculation does not consider effects of any dilutive securities in computation of EPS:
revenue average working capital
Gross, operating, and net profit margins: ~ . gross profit gross profit margin = —----- i-----revenue ^ . operating profit EBIT operating profit margin = —--------—------ — revenue net sales net profit margin =
basic EPS =
net income —preferred dividends wtd. avg. no. of common shs. outstanding
diluted EPS =
Return on assets [return on total capital (ROTC)]:
Debt to equity ratio and total debt ratio: debt-to-equity ratio =
wtd shares from sh ’s from shares avp + conversion of + conversion + issuable from sh s conv. pfd. sh ’s ^conv. debt / stock options
net profit asset equity margin turnover multiplier
Extended DuPont equation further decomposes net profit margin: net income v E B T ) v ' EBIT A A revenue / EBT EBIT 2 revenue avg. total assets vA x avg. total assets avg. equity
You may also see it presented as: ROE = tax burden x interest burden x EBIT margin x asset turnover x leverage Marketable Security Classifications Held-for-trading: fair value on balance sheet; dividends, interest, realized and unrealized G/L recognized on income statement. Available-for-sale: fair value on balance sheet; dividends, interest, realized G/L recognized on income statement; unrealized G/L is other comprehensive income.
(cost —accum. depreciation)
Units o f production: cost —salvage value -------------------------- X output units useful life in units
kassets, , equity /
You may also see it presented as:
DuPont Analysis Traditional DuPont equation:
return on equity =
Long-Lived Assets Capitalizing vs. Expensing Capitalizing: lowers income variability and increases near-term profits. Increase assets, equity. Expensing: opposite effect.
Liquidity ratios indicate company’s ability to pay its short-term liabilities. Operating performance ratios indicate how well management operates the business.
return on equity =
adj. income avail, for common shares wtd. avg. common shares plus potential common shares outstanding
Therefore, diluted EPS i s : < fJi convertible convertible net _ prd + preferred + debt (1- t ) income div dividends interest
return on assets _ EBIT (total capital) average total capital
purchases average trade payables
Held-to-maturity: amortized cost on balance sheet; interest, realized G/L recognized on income statement.
Total asset, fixed-asset, and working capital turnover ratios: revenue total asset turnover = average total assets
Revaluation o f Long-Lived Assets IFRS: revaluation gain recognized in net income only to the extent it reverses previously recognized impairment loss; further gains recognized in equity as revaluation surplus. (For investment property, all gains and losses from marking to fair value are recognized as income.) U S. GAAP: revaluation is not permitted. Deferred Taxes • Created when taxable income (on tax return) ^ pretax income (on financial statements) due to temporary differences. • Deferred tax liabilities are created when taxable income < pretax income. Treat DTL as equity if not expected to reverse. • Deferred tax assets are created when taxable income > pretax income. Must recognize valuation allowance if more likely than not that DTA will not be realized. Long-Term Liabilities • Premium bond: coupon rate > market rate at issuance. • Discount bond: coupon rate < market rate at issuance. • Interest expense equals book value at the beginning of the year multiplied by the market rate of interest at the time the bonds were issued.
Leases Financial statement!ratio impact of lease accounting from the lessee perspective: capital leases result in: • Higher: assets, liabilities, CFO, debt/equity. • Lower: net income (early years), CFF, current ratio, working capital, asset turnover, ROA, ROE. • Same: total cash flow. Pensions Defined contribution: employer contribution expensed in period incurred. Defined benefit: overfunded plan recognized as asset, underfunded plan recognized as liability.
Cost of trade credit: % discount 1—% discount
365 days past discount
Corporate Governance One-tier board: Includes internal and external directors Two-tier board: Supervisory board of external directors, management board of internal directors Board committees: Audit: Financial reporting Governance: Legal and ethics compliance Nominations: Find Board candidates Remuneration: Compensation for senior managers Risk: Firm risk tolerance and risk management Investment: Review large capital projects, asset purchases, asset sales
CORPORATE FINANCE W eighted Average Cost o f Capital WACC = (wd) [kd (1-t)] + (wps )(kps) + (wce)(ks) Cost o f Preferred Stock
+g o Cost o f Equity Using CAPM k e = RFR + ^ ( R mtt - RFR) Capital Budgeting NPV - CF0 +
CFl . + CFz (1 + k )1 (l + k);
CF" (1 + k)n
IRR: discount rate that makes NPV equal to zero. Pure-Play M ethod Project Beta Delevered asset beta for comparable company: 1 P aasset sse t
P ^ e q u ity
Com bining Preferences with the Optimal Set o f Portfolios Markowitz efficient frontier is the set of portfolios that have highest return for given level of risk. E(Rp)
CAPM : E(Rj) = RFR + j3- [E(Rmkt) - RFR E(Ri)
The SML and Equilibrium Identifying mispriced stocks: Consider three stocks (A, B, C) and SML. Estimated stock returns should plot on SML. • A return plot over the line is underpriced. • A return plot under the line is overpriced. E(R)
RFR 0 risk
1 Risk-Adjusted Returns Sharpe ratio and M-squared measure excess return per unit of total risk. Treynor measure and Jensens alpha measure excess return per unit of systematic risk. E(R)
i+ (i-0 v ' e Relevered project beta for subject firm: D 0project . = 0 r-'nroiecr asset X 1 + ( i - t ) r^ '
Measures o f Leverage Total leverage: percent change in net income from a given percent change in sales. Operating leverage: percent change in EBIT from a given percent change in sales. Financial leverage: percent change in net income from a given percent change in EBIT.
Security Market Line (SML) Investors should only be compensated for risk relative to market. Unsystematic risk is diversified away; investors are compensated for systematic risk. The equation of the SML is the CAPM, which is a return/systematic risk equilibrium relationship. total risk = systematic + unsystematic risk
breakeven quantity of sales = Fixed operating & financing costs price —variable costs per unit
SECURITIES MARKETS & EQUITY INVESTMENTS
operating breakeven quantity of sales = fixed operating costs price —variable costs per unit Working Capital Management Primary sources ofiliquidity, cash balances, short-term funding, cash flow management of collections and payment. Secondary sources ofiliquidity, liquidating assets, negotiating debt agreements, bankruptcy protection.
W ell-Functioning Security Markets • Operational efficiency (lowest possible transactions costs). • Informational efficiency (prices rapidly adjust to new information). RFR
Critical relationship between k and g : • As difference between ke and gc widens, value of stock falls. • As difference narrows, value of stock rises. • Small changes in difference between ke and gc cause large changes in stock’s value. Critical assumptions of infinite period DDM: • Stock pays dividends; constant growth rate. • Constant growth rate, g , never changes. • k must be greater than g (or math will not work)
Com puting Index Prices „ . •i it j S stock prices Price-weighted Index = —---------— adjusted divisor Value-weigh ted Index XXcurrent prices) (# shares) . . = --------------------- 4-------------------------- x base value XXbase year prices)(#base year shares) Types o f Orders Execution instructions: how to trade; e.g., market orders, limit orders. Validity instructions: when to execute; e.g., stop orders, day orders, fill-or-kill orders. Clearing instructions: how to clear and settle; for sell orders, specify short sale or sale of owned security.
EQUITY INVESTMENTS Industry Life Cycle Stages Embryonic: slow growth, high prices, large investment needed, high risk of failure. Growth: rapid growth, falling prices, limited competition, increasing profitability. Shakeout: slower growth, intense competition, declining profitability, cost cutting, weaker firms fail or merge. Mature: slow growth, consolidation, stable prices, high barriers to entry. Decline: negative growth, declining prices, consolidation. Five Competitive Forces 1. Rivalry among existing competitors. 2. Threat of entry. 3. Threat of substitutes. 4. Power of buyers. 5. Power of suppliers. One-Period Valuation Model D, (l + k„)
(l + k_)
Be sure to use expected dividend
Infinite Period Dividend D iscount Models Supernormal growth model (multi-stage) DDM: V0 =
(1 + k„)
where: Pn =
+ D n+1
(k e Sc) Constant growth model: v _ P pfl + gc) _ 0 1 ke - g c
Dn (i + k e)n
n d + k e)n
Bond Markets National bond market includes domestic bonds and foreign bonds. • Domestic bonds. Domestic issuer and currency. • Foreign bonds. Foreign issuer, domestic currency. Eurobond market is outside any one country, with bonds denominated in currencies other than those of countries in which bonds are sold. Global bonds trade in both a national bond market and the eurobond market.
Earnings Multiplier Model D i _ payout ratio o_ k -g
Market Structures Quote-driven markets: investors trade with dealers. Order-driven markets: buyers and sellers matched by rules. Brokered markets: brokers find counterparties. Forms o f EM H • Weakform. Current stock prices fully reflect available security market info. Volume information/past price do not relate to future direction of security prices. Investor cannot achieve excess returns using tech analysis. • Semi-strongform. Security prices instantly adjust to new public information. Investor cannot achieve excess returns using fundamental analysis. • Strongform. Stock prices fully rfleet all information from public and private sources. Assumes p efect markets in which all information is cost free and available to everyone at the same time. Even with inside info, investor cannot achieve excess returns.
full price = PV at last coupon date x (1 + YTM)r/I accrued interest = coupon payment x (t/T) where: t = days from most recent coupon payment to trade settlement T = days in coupon payment period Matrix pricing: For illiquid bonds, use yields of bonds with same credit quality to estimate yield; adjust for maturity differences with linear interpolation.
leading P/E = trailing P/E =
price per share
book value per share price per share sales per share price per share cash flow per share
Bond Issuance Underwritten offering: Investment banks buy entire issue, sell to public. Best efforts offering: Investment banks act as brokers. Shelfregistration: Register entire issue with regulators but sell over a period of time.
EPS previous 12 mo.
price per share
price per share forecast EPS next 12 mo.
Basic Features o f Bonds Issuer. Sovereign, non-sovereign, quasi-government, supranational, corporate, SPE. Maturity. Money market (one year or less); capital market (greater than one year). Par value. Bond’s principal value (face value). Coupon. Annual percent of par; fixed or floating. Divide by periodicity to get periodic rate. Currency. Single, dual, currency option. Indenture. Affirmative and negative covenants. Price, Yield, Coupon Relationships Bond prices and yields are inversely related. Increase in yield decreases price; decrease in yield increases price. Coupon < yield: Discount to par value. Coupon > yield: Premium to par value. Constant-yield price trajectory: Price approaches par as bond nears maturity from amortization of discounts and premiums. Capital gains and losses are calculated relative to this trajectory. Cash Flow Structures Bullet: All principal repaid at maturity. Fully amortizing: Equal periodic payments include both interest and principal. Partially amortizing: Periodic payments include interest and principal, balloon payment at maturity repays remaining principal. Sinking fund: Schedule for early redemption. Floating-rate: Coupon payments based on reference rate plus margin. Bond Pricing There are two equivalent ways to price a bond: • Constant discount rate applied to all cash flows (YTM) to find PV. This is a bond’s fla t price (does not include accrued interest). • Discount each cash flow using appropriate spot rate for each. This is a bond’s no-arbitrage price. Full price includes accrued interest. Government bonds use actual day counts; corporate bonds use 30/360 method.
Embedded Options Callable: Issuer may repay principal early. Increases yield and decreases duration. Putable: Bondholder may sell bond back to issuer. Decreases yield and duration. Convertible: Bondholder may exchange bond for issuer’s common stock. Embedded warrants: Bondholder may buy issuer’s common stock at exercise price. Yield Measures Effective yield depends on periodicity. YTM = effective yield for annual-pay bonds. Semiannual bond basis: YTM = 2 x semiannual discount rate. Current yield = annual coupon / price. Simple yield = current yield ± amortization. Yield to call is based on call date and call price. Yield to worst is lowest of a bond’s YTCs or YTM. Money market yields may be on a discount or addon basis and may use a 360- or 365-day year. Bond-equivalent yield is an annualized add-on yield based on a 365-day year. Forward and Spot Rates Forward rate is a rate for a loan that begins at a future date. “Iy3y” = 3-year forward rate 1 year from today. Example of spot-forward relationship:
(1 + S2)2 = (1 + S,)(l + lyly) Yield Spreads G-spread: Basis points above government yield. I-spread: Basis points above swap rate. Z-spread: Accounts for shape of yield curve. Option-adjusted spread: Adjusts Z-spread for effects of embedded options. Interest Rate Risk Interest rate risk has two components: reinvestment risk and market price risk from YTM changes. These risks have opposing effects on an investor’s horizon yield. • Bond investors with short horizons are more concerned with market price risk. • Bond investors with long horizons are more concerned with reinvestment risk. • The horizon at which market price risk and reinvestment risk just offset is a bond’s Macaulay duration. This is the weighted average of times until a bond’s cash flows are scheduled to be paid.
Modified duration is the approximate change in a bond’s price given a 1% change in its YTM: Macaulay duration
0 + r)
(V -)-(V .) 2V0 (Ay)
Effective duration is required if a bond has embedded options: (V -)-(V + ) 2V q (Acurve) Price change estimates based on duration only are improved by adjusting for convexity: 1 %Aprice = —duration (Ay) H— convexity (Ay)' Asset-Backed Securities Residential M BS: home mortgages are collateral. Agency RMBS include only conforming loans; nonagencv RMBS may include nonconforming loans and need credit enhancement. Prepayment risk: contraction risk from faster prepayments; extension risk from slower prepayments. CMOs: pass-through MBS are collateral. May have sequential-pay or PAC/support structure. Commercial MBS: non-recourse mortgages on commercial properties are collateral. Auto ABS: auto loans are collateral. Credit card ABS: credit card receivables are collateral. CDOs: Bonds, bank loans, MBS, ABS, or other CDOs are collateral. Collateral and Credit Enhancement Secured bonds are backed by specific collateral and senior to unsecured bonds. Unsecured bonds are general claims to issuer’s cash flows and assets. Internal credit enhancement: Excess spread, overcollateralization, waterfall structure. External credit enhancement: Surety bonds, letters of credit, bank guarantees. Credit Analysis Investment grade: Baa3/BBB—or above Non-investment grade: Bal/BB+ or below Corporate family rating (CFR): issuer rating. Corporate credit rating (CCR): security rating. “Four Cs”: capacity, collateral, covenants, character, default risk = probability of default loss severity = percent of value lost if borrower defaults expected loss = default risk x loss severity recovery rate = 1 —expected loss percentage
DERIVATIVES Arbitrage and Replication • Law o f one price: two assets with identical cash flows in the future, regardless of future events, should have the same price. • Two assets with uncertain returns can be combined in a portfolio that will have a certain payoff. If a portfolio has a certain payoff, the portfolio should yield the risk-free rate. For this reason, derivatives values are based on risk-neutral pricing. Derivatives Values vs. Prices The price of a forward, futures, or swap contract is the forward price stated in the contract and is set such that the contract has a value of zero at initiation. Value may change during the contract’s life with opposite gains/losses to the long and short.
Forward Contract Value At time t. Fq (T)
Vt (T) = St + PVt (cost) - PVt (benefit)
(1 + Rf)T -t
A t expiration (time t = T): payoff to long = S.r - FQ(T) Futures vs. Forwards Forwards Private contracts Unique contracts Default risk Little or no regulation
Futures Exchange-traded Standardized contracts Guaranteed by clearinghouse Regulated
Forward Rate Agreements (FRA) Can be viewed as a forward contract to borrow/ lend money at a certain rate at some future date. Interest Rate Swaps May be replicated by a series of off-market FRAs with present values at swap initiation that sum to zero. Options • Buyer of a call option— long asset exposure. • Writer (seller) of a call option— short asset exposure. • Buyer of a put option— short asset exposure. • Writer (seller) of a put option— long asset exposure. intrinsic value of a call option = Max[0, S —X] intrinsic value of a put option = Max[0, X —S] American vs. European Options American options allow the owner to exercise the option any time before or at expiration. European options can be exercised only at expiration. Value of American option will equal or exceed value of European option. They will have identical values except for: (1) call options on dividend paying stocks and (2) in-the-money put options. Factors that Affect O ption Values Increase in:
Time to expiration
*Except some deep-in-the-money European puts. Put-Call Parity The put-call parity relationship for European options at time tr. X ct + 7 ~7f"— St + pt (l + R f)T
ALTERNATIVE INVESTMENTS Hedge Funds Event-driven strategies: merger arbitrage; distressed/ restructuring; activist shareholder; special situations. Relative value strategies: convertible arbitrage; asset-backed fixed income; general fixed income; volatility; multi-strategy. Equity strategies: market neutral; fundamental growth; fundamental value; quantitative directional; short bias. Macro strategies: based on global economic trends. Hedge fund fees: • “2 and 20”: 2% management fee plus 20% incentive fee. • Hard hurdle rate: incentive fee only on return above hurdle rate. • Soft hurdle rate: incentive fee on whole return, but only paid if return is greater than hurdle rate. • High water mark: no incentive fee until value exceeds previous high. Private Equity Leveraged buyouts: management buyouts (existing managers), management buy-ins (new managers) Venture capital stages of development: • Formative stage: angel investing, seed stage, early stage. • Later stage: finance product development, marketing, market research. • Mezzanine stage: prepare for IPO. Portfolio company valuation methods: market/ comparables; discounted cash flow; asset-based. Exit strategies: trade sale; IPO; recapitalization; secondary sale; write-off. Real Estate Includes residential property; commercial property; real estate investment trusts (REITs); farmland/ timberland; whole loans; construction loans. Property valuation methods: comparable sales; income approach; cost approach. Commodities Contango: futures price > spot price. Backwardation: futures price < spot price. Sources of investment return: • Collateralyield: return on T-bills posted as margin. • Price return: due to change in spot price. • Rollyield: positive for backwardation, negative for contango. futures price « spot price (1 + Rf) + storage costs —convenience yield Infrastructure Long-lived assets for public use, including transportation, utility, communications, social Brownfield: Existing infrastructure Greenfield: Infrastructure to be built